Ben Crowell
Reputation
30,975
105/100 score
 Aug 16 comment With redshift, energy is lost. Where does it go? My argument above relates to reference frames and does not discuss expansion of space itself as in cosmological models. But that's what the question is about. This answer doesn't address the question. May 21 comment Why Negative Energy States are Bad This is total nonsense. The definitions proposed here are not even viable definitions, because they don't handle the zero-mass case. The relativistic relation that works for all masses, including zero mass, is $m^2=E^2-p^2$, which is perfectly compatible with $E<0$. If this elementary classical argument had been correct, then it would have been a schoolboy mistake for Dirac to propose his picture of the Dirac sea. Feb 11 comment How come some people are claiming that the Big Bang never happened? This doesn't address the question. Jan 2 comment Energy Required to Rip Spacetime It sounds like you're referring to topology change. The classic paper on this topic is by Geroch, adsabs.harvard.edu/abs/1967JMP.....8..782G . Here is a more recent discussion: arxiv.org/abs/gr-qc/9406053 . Geroch showed that there must be either CTCs or a violation of the weak energy condition. Dec 29 comment Why are electromagnetic waves not able to pass through a hole with a diameter smaller than the wavelength? But if they are close together...closer than the wavelength of the radiation...then they represent two coherent sources whose amplitudes add. So you get FOUR times the power. Diameter-to-the-fourth. (Because it doesn't matter if the two holes are merged into one.) Two mistakes here. (1) Two holes side by side do not constitute a hole with twice the diameter. (2) If power goes like the fourth power of the diameter, and you double the diameter, then you get 16 times the power, not four times. For a correct explanation of the exponent, see the questions that this question duplicates. Dec 27 comment Why are electromagnetic waves not able to pass through a hole with a diameter smaller than the wavelength? Dec 7 comment Has relativity of simultaneity been directly observed? [...] test theory, which is provided by the SME of Colladay and Kostelecky, arxiv.org/abs/hep-ph/9809521 . A vast amount of data has tightly constrained the Lorentz-violating parameters of the SME: arxiv.org/abs/0801.0287 Dec 7 comment Has relativity of simultaneity been directly observed? [...] simultaneity becomes absolute in that sense. That doesn't mean that the many tests of the relativity of simultaneity become invalidated. We've experimentally verified that different observers get different results when they carry out synchronization. A preferred frame would just tell us that one privileged observer's result was preferred. Furthermore, RMS is purely a kinematic theory, and therefore its parameters would be specific to a certain measuring device, such as a specific kind of clock. Null results from clock-comparison experiments tell us that we really need a dynamical [...] Dec 7 comment Has relativity of simultaneity been directly observed? This is a misinterpretation both of the RMS test theory and of this type of test theory in general. In the current fundamental theories of physics, Lorentz invariance is taken to be exact, and that means that regardless of the precision with which we can verify LI, it is still vulnerable to falsification by a later, more precise experiment. Any such hypothetical future falsification of LI would presumably lead to the existence of a preferred frame, since LI is mainly a statement of the nonexistence of preferred frames. Given a preferred frame, we have a preferred time coordinate, and [...] Nov 22 comment Would a wormhole in space look like anything at all? @GreenAsJade: Intense radiation inside the wormhole is a standard prediction. I don't know enough about QFT on a curved background to be able to give you a clear explanation. Nov 21 comment Would a wormhole in space look like anything at all? What you're saying makes sense to me. I would also probably expect a wormhole to emit a lot of nasty ionizing radiation, since that's what's normally expected to destroy objects passing through. Nov 21 comment Definition of the $Q$ factor? Why the downvote? Nov 21 comment How far has a 13.7 billion year old photon travelled @PetTaxi: The proper length is zero, because the photon's path is lightlike. If you want to define the photon's "odometer," you can't do it in the photon's frame, because a photon doesn't have a rest frame. The 13.7 byr is measured on a clock that's at rest relative to the Hubble flow. The 13.7 blyr is measured on a chain of rulers, each at rest relative to the Hubble flow. Nov 21 comment Do consciousnesses get “scattered” across the many worlds of the MWI? MWI doesn't really have branching. physics.stackexchange.com/questions/32501/… . MWI just says there's a wavefunction, and it evolves unitarily. Branching may be an appropriate, approximate description in some cases. Nov 21 comment What is wrong with the Bohr model? It predicts that the hydrogen atom is flat rather than spherical. It predicts the wrong angular momenta, e.g., $L=1\hbar$ for the ground state rather than the correct $L=0$. Nov 21 comment How to theoretically define a concrete operation to perform in order to measure the length of an object? @bobie: does your post answer the OP question? Yes, it does. See the paragraph beginning with "Einstein synchronization..." Nov 21 comment How to theoretically define a concrete operation to perform in order to measure the length of an object? @user12262 and bobie: You might benefit from reading the linked article on operationalism. Nov 21 comment Why is the energy of particles in accelerators much higher than the energy of the particles they are trying to find? The multiplicity of charged hadrons produced in pp collisions at the LHC seems to be $\sim100$: dspace.mit.edu/handle/1721.1/68876 . If you're producing on the order of a hundred particles, maybe it makes sense that you have to put in on the order of a hundred times the energy of the particle you're hoping to create. Nov 20 comment Center of mass of two $\gamma$ rays moving in opposite directions Nice. Another way of looking at this is that the energy-momentum vector of the system as a whole is $(E,p)=(\omega_1+\omega_2,\omega_1-\omega_2)$, in units where $\hbar=1$. The boost needed in order to make this vector purely timelike is $v=p/E$. Nov 20 comment Expansion rate in matter dominated era When you ask for the expansion rate, are you asking for the Hubble constant?